ABSTRACT
Let Ω ⊂ ℝ n be a bounded open set with C 2 boundary ∂Ω and exterior unit normal vector ν. Let ρ be a T-periodic positive C 1 function, and let A : D ( A ) = { φ ∈ H 2 ( Ω ) : ∂ φ ∂ ν = 0 } → L 2 ( Ω ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141244/9531f423-8a2f-453c-a111-77ec08caec6c/content/iequ17_1.tif"/> , Aφ = Δφ be the realization of the Laplace operator in L 2(Ω) with homogeneous Neumann boundary condition. We shall study the stabilizability problem for the strongly damped wave equation and the proportionally damped wave equation in (0, +∞) × Ω :
